In this paper we have developed the quintic B-spline basis functions based differential quadrature method for the numerical solution of nonlinear Schrödinger equation. The numerical simulations such as motion of single solitary wave, interaction of two solitary waves, generation of solitary waves using the Maxwellian initial condition, birth of mobile soliton, bound state of solitons have been carried out and results are compared with the analytical solution and some published work. Conserved quantities are also computed numerically for all cases. The stability is discussed using matrix stability method. The scheme is found stable and provides very accurate results as compared to other numerical techniques. © 2017, Springer (India) Private Ltd., part of Springer Nature.